Question: Rewrite as a simplified fraction. ${2.4\overline{27} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2427.2727...\\ 10x &= 24.2727...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2403}$ ${x = \dfrac{2403}{990}} $ ${x = \dfrac{267}{110}} \text{or} {2 \dfrac{47}{110}}$